The discovery of Dirac electrons in graphene has initiated the search for new types of two-dimensional (2D) materials which exhibit quantum properties distinct from those of bulk counterparts [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. Atomically-thin transition-metal dichalcogenides (TMDs) are attracting particular attention not only because parent bulk TMDs exhibit various physical properties, but also because the two-dimensionalization of TMDs leads to outstanding characteristics such as Ising superconductivity [9]}, spin-valley Hall effect [6]}, and 2D Mott-insulating phase [10]}, [11]}. To fully explore unique features of 2D TMDs, it is essential to compare the electronic properties between 2D and 3D systems and obtain insight into the evolution of physical properties upon the dimensional crossover. In this context, one may expect a similar electronic property between 2D and 3D cases because bulk TMDs are a layered quasi-2D system. In fact, similarity between monolayer and bulk has been identified in some TMDs, as highlighted by the 2\(\times \) 2 charge-density wave (CDW) in 1\(T\) -TiSe\(_2\)  accompanied by the exciton condensation [16]}, [17]}, the superconductivity coexisting with CDW in 1\(H\) /2\(H\) -NbSe\(_2\) ,[6]} and the CDW associated with Star-of-David clusters in 1\(T\) -TaSe\(_2\) .[19]} On the other hand, some 2D TMDs exhibit electronic properties that cannot be understood simply by extending the framework of 3D system, as represented by monolayer (ML) 1\(T\) -VSe\(_2\)  with a variety of periodic lattice distortions (PLD; e.g. 4\(\times \) 4, 4\(\times \) 1, \(\sqrt{7}{\times }\sqrt{3}\) , 4\(\times \sqrt{3}\) ) [20]}, [21]}, [22]}, [23]}, [24]} which are hardly explained in terms of a simple Fermi-surface (FS) nesting picture, different from the nesting-driven 4\(\times 4{\times }{\sim }3\)  CDW in bulk 1\(T\) -VSe\(_2\) . [25]}, [26]}, [27]}, [28]}, [29]}
